A mixed number is a combination of a whole number and a proper fraction. It is usually expressed as a whole number plus a fraction. An example of a mixed number is three and one-half, written as 3 ½. Expressing a fraction in its simplest form is a very important concept in mathematics. Simplifying a fraction means to reduce it to its lowest terms, or its most basic form. To express 105 20 as a mixed number in its simplest form, it must first be converted into an improper fraction.

## Converting an Improper Fraction

In order to convert an improper fraction to a mixed number, the numerator must be divided by the denominator. The quotient is the whole number part of the mixed number, while the remainder is the numerator of the fractional part. To express 105 20 as a mixed number in its simplest form, the numerator, 105, needs to be divided by the denominator, 20.

105 divided by 20 is 5 with a remainder of 5. Thus, 105 20 can be expressed as a mixed number in its simplest form as 5 5/20. The whole number part is 5 and the fractional part is 5/20. Since 5 is the numerator and 20 is the denominator, 5/20 is already in its simplest form. This expression can be further simplified by writing it as a decimal, which is 5.25.

## Simplifying Fractions

To express a fraction in its simplest form, the numerator and denominator must both be divided by their greatest common factor, or GCF. This is a number which divides both the numerator and denominator evenly, with no remainder. An easy way to determine the GCF of two numbers is to list the factors of each and then find the largest number that is common to both. For example, the factors of 20 are 1, 2, 4, 5, 10 and 20. The factors of 5 are 1 and 5. The greatest common factor of both is 5.

When the GCF of both numbers is determined, it can be divided into both the numerator and denominator. In the case of 5/20, 5 is divided by 5 and 20 is divided by 5. This simplifies the fraction to 1/4. The fraction is now in its simplest form.

Expressing a fraction in its simplest form is essential for understanding basic mathematics. Expressing 105 20 as a mixed number in its simplest form can be achieved by first converting it to an improper fraction. The numerator of the improper fraction can then be divided by the denominator to get the whole number part of the mixed number. Finally, the numerator and denominator can be divided by their greatest common factor to simplify the fraction to its lowest terms.

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